==================================== timezone-relative day count for Mars ==================================== by Andrew Main (Zefram) 2007-02-17 abstract -------- Terran calendarists have found a need for a timezone-relative version of astronomers' absolute day count systems, and have defined such systems. The same need exists in Martian timekeeping. An absolute day count for Mars exists in the form of the Mars Sol Date (MSD), but there appears to be no established convention for a timezone-relative day count for Mars. This memo therefore defines the Chronological Mars Solar Date (CMSD), with the equation CMSD = MSD + 500000 + Zoff, where Zoff is the timezone offset in fractional days. Related quantities are also defined. table of contents ----------------- 0. need 0.0. Terra 0.1. Mars 1. definitions 2. references 0. need ======= 0.0. Terra ---------- In situations where calendars are a distraction, such as astronomy, it is often preferred to track time by a simple linear count of days elapsed since a well-known epoch. For example, the Julian Date (JD) is defined as the number of days elapsed since -4713-11-24T12 UT (proleptic Gregorian calendar). JD and its derivatives are widely used in scientific disciplines related to astronomy and timekeeping. Calendarists and historians have a similar requirement, differing in an important detail. It is useful to them to express civil dates in a calendar-neutral manner, in the form of a linear count of days. Civil dates are usually relative to local solar time, or since the nineteenth century relative to a locally-mandated timezone. A timezone-relative day count allows comparison of civil dates across timezones (as opposed to comparing absolute points in time), and allows a date to be expressed when its timezone is unknown. An example of a timezone-relative day count system is the Chronological Julian Date, described in [JDN] and [CJD-MSG]. It is defined, for any particular timezone, by the equation CJD = JD + 0.5 + Zoff where Zoff is the offset of the timezone's time of day from the UT time of day, expressed in fractional days. 0.1. Mars --------- As the study of the planet Mars has progressed, a need to track Martian solar time has developed. Lander missions, particularly, are affected by the diurnal cycle, for reasons of visibility and the availability of solar power. Among those who must deal with Martian and Terran days at the same time, Martian days are referred to as "sols". A prime meridian has been defined for Mars, passing through the centre of the small crater Airy-0 in Meridiani Planum [AIRY-0]. Mean solar time on the Martian prime meridian is known as Airy Mean Time (AMT), by analogy with Greenwich Mean Time (GMT), or misleadingly as Coordinated Mars Time (MTC), by faulty analogy with Coordinated Universal Time (UTC) [MARS24-TN]. A Martian solar day count has been defined: the Mars Sol-Date (MSD) [RECIPE]. The MSD is a count of Martian solar days since approximately JD 2405521.00 in Terrestrial Time, the epoch being chosen for the near-coincidence of Airy mean midnight with Greenwich mean noon. The MSD takes an integral value at each mean midnight on the Airy meridian. Martian lander missions have adopted the Terran civil convention of referring to local mean solar time, rather than using a single time scale (AMT) at all longitudes. In fact, the rovers Spirit and Opportunity have notably not used precisely mean solar time at any point in the immediate vicinity of the landing site or anticipated operational areas. Rather, they have adopted the mean solar time of a nearby longitude, chosen to closely match the apparent solar time of the landing site at the middle of the nominal mission period [MARS24-TN]. The Mars Exploration Rover missions are thus using timezones. They also identify each Martian day by an integral number, incrementing uniformly, with the day of landing identified as "sol 1" [MARS24-TN]. The days identified by these numbers extend from midnight to midnight in the mission timezone, and are not tied to AMT. The day counts are not aligned with each other; they are established separately for each lander. These lander mission day counts each have the semantics of a timezone-relative integral day count, analogous to the Chronological Julian Day Number (CJDN) for Terra. Comparison of dates between missions would be facilitated by using a single epoch for all missions. In anticipation of the need for seasonal timekeeping on Mars, there have been several proposals for calendars to reconcile the Martian day with the Martian tropical year [CALENDARS]. In fact such a need already exists: the rover missions are affected by the variable availability of solar power over the course of the year. As on Terra, the definition and comparison of calendars would be facilitated by a calendar-neutral timezone-relative linear day count. No such timezone-relative day count appears to exist for Mars, except for the various mission-specific counts used with landers. 1. definitions ============== The Chronological Mars Solar Date (CMSD) is defined, for any particular timezone, by the equation CMSD = MSD + 500000.0 + Zoff where Zoff is the offset of the timezone's time of day from the AMT time of day, expressed in fractional days. The constant offset of 500000 is included so that CMSD and MSD values are unlikely to be mistaken for each other: any such confusion would result in dates almost 750 Martian years wrong, which should be quickly noticed. Example (all numbers approximate): the Opportunity rover mission uses a timezone of AMT-01:01, and so has Zoff = -0.042. The rover landed in Meridiani Planum at MSD 46236.600. The landing time can thus be expressed as CMSD 546236.558 in the mission timezone. The CMSD may be separated into integral and fractional parts. The integer part is the Chronological Mars Solar Day Number (CMSDN), and the fractional part is the Chronological Mars Solar Day Fraction (CMSDF). They are related by the equation CMSD = CMSDN + CMSDF where CMSDN is constrained to be an integer and CMSDF is constrained to be in the range [0, 1). Example: Opportunity's landing occurred on CMSDN 546236 in the mission timezone. That is labelled as "sol 1" in the context of the mission, so the mission sol number can be defined as CMSDN - 546235. The time of day of the landing was CMSDF 0.558 in the mission timezone, corresponding to 13:23 on the 24-hour clock. (Time of day approximate.) 2. references ============= [AIRY-0] Malin Space Science Systems, "The Martian Prime Meridian -- Longitude "Zero"", MGS MOC Release No. MOC2-273, 31 January 2001, . [CALENDARS] Thomas Gangale, "Martian Calendars", . [CJD-MSG] Peter Meyer, "Message Concerning Chronological Julian Days/Dates", 23 Jan 2004, . [JDN] Peter Meyer, "Julian Day Numbers", . [MARS24-TN] Michael Allison and Robert Schmunk, "Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock", Dec. 13 2005, . [RECIPE] Michael Allison and Megan McEwen, "A post-Pathfinder evaluation of aerocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies", 16 August 1999, Planetary and Space Science 48 (2000), 215-235, .